Question 9
If $k,m,n$ are integers such that $2\le k\le m\lt n$, show that
$$\frac{m!}{m^k(m-k)!}\lt \frac{n!}{n^k(n-k)!}.$$
Note that $0!=1$ and $r!=1\times2\times3\times\cdots\times r$ for any positive integer $r$.
$$\frac{m!}{m^k(m-k)!}\lt \frac{n!}{n^k(n-k)!}.$$
Note that $0!=1$ and $r!=1\times2\times3\times\cdots\times r$ for any positive integer $r$.